Abstract
We propose a numerical approach that combines a radial basis function (RBF) meshless approximation with a finite difference discretization to solve a nonlinear system of integro-differential equations. The equations are of advection-reaction-diffusion type modeling the formation of pre-cartilage condensations in embryonic chicken limbs. The computational domain is four dimensional in the sense that the cell density depends continuously on two spatial variables as well as two structure variables, namely membrane-bound counterreceptor densities. The biologically proper Dirichlet boundary conditions imposed in the semi-infinite structure variable region is in favor of a meshless method with Gaussian basis functions. Coupled with WENO5 finite difference spatial discretization and the method of integrating factors, the time integration via method of lines achieves optimal complexity. In addition, the proposed scheme can be extended to similar models with more general boundary conditions. Numerical results are provided to showcase the validity of the scheme.
Highlights
A central question in several areas of biology is how populations of cells interact to form various complex structures
Several modeling approaches for cell-cell adhesion have been proposed in this continuous framework [5,6,7,8], the most widely adopted being that of Armstrong et al [5] based on a nonlocal adhesion flux term
We study an advection-reaction-diffusion system modeling the formation of cell aggregations in cultures of embryonic chicken limbs proposed in [17]
Summary
A central question in several areas of biology is how populations of cells interact to form various complex structures. Examples include organogenesis in developmental biology [1,2] or tumor growth in cancer research [3,4] These phenomena typically span several spatial and temporal scales and involve interactions of many different processes, such as undirected or directed cell motion, cell-cell adhesion, gene expression and the transport of various molecules by diffusion or advection. Several modeling approaches for cell-cell adhesion have been proposed in this continuous framework [5,6,7,8], the most widely adopted being that of Armstrong et al [5] based on a nonlocal adhesion flux term Most prominently, this has been applied in the area of tumor modeling and cancer invasion, see, e.g., [9,10,11,12,13,14,15]. A similar approach was used to model the formation of liver cell aggregations in vitro [16]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
